There is no right or wrong ... once you have achieved a reasonable mastery of technique. Until then, there is a choice of what's easiest at the time versus what will get you to that "reasonable mastery" point. To use great musicians using unconventional methods as examples to emulate might be misleading to beginners.
As already stated, index-and-middle is the most conventional method, used by the majority of players; it will get you to "reasonable mastery" efficiently in most music (and perhaps because it came from the double bass). Once you learn that technique, feel free to use thumb, pick, and/or anything else.
Interesting that you name Carl Wilson ... I wouldn't put him on a level with the other greats you mention. Yes, many bassists used their thumbs when the bass guitar was new; I suggest that it's because their parts were simple. I use my thumb sometimes for simple parts, only because I like that sound for particular things.
'Reasonable mastery' is going to take me a long time but, with my limited ability I'm going to have to accept that. I appreciate your input.